Supplemental Materials For: Assessment of goose-beaked whale responses to mid-frequency active sonar using a hierarchical hidden Markov model

Supplemental Tables

Dive-cycle Summary

Table S1: Summary information about each foraging dive cycle included in the HHMM analysis.

MFAS exposure details

Table S2: MFAS exposure data summarised by SMRT tag deployment. Note that dive cycles where acoustic audits indicated MFAS presence, but for which SNR was too low to report any measures RMS or cSEL values, are not included in this table.

Variant State Occurrence per MFAS-exposed Dive Cycle

Table S3: Occurrence of Variant state for each dive cycle that contained detected MFAS sounds. The “State” column indicates the current dive-cycle-level state, while the “Switched to Variant State?” column indicates whether or not the whale switched from Typical to Variant state during the current dive cycle. In six cases, the whale was already in Variant state before the dive cycle with MFAS began, and then remained in Variant state during the exposed dive cycle; these rows have “Started Earlier” in the “Switched to Variant State?” column.

Here, we see that whales transitioned to Variant state in 12 out of 52 MFAS-exposed dive cycles (23.1 percent).

If we consider only dive cycles where the MFAS cSEL was above 110 dB re 1\(\mu Pa^2*sec\), then that becomes 12 out of 40 MFAS-exposed dive cycles (30 percent).

MFAS Received Level Data Table

All received level values (for each received sound, as opposed to summarised over 5-minute or dive-cycle periods) are also available as text files.

File name: mfas-raw-rls.csv (located in the data directory).

Note: Each table printed above is also available as a text file in the data directory.

Tallying 5-Minute States

Table S4: Occurrences of each of the four states at the five-minute timescale, by HHMM state and MFAS presence.

Duration of Variant State

Data Variant State Bouts

Table S5: Variant state bouts observed in the SMRT data, according to the fitted HHMM.

Figure S1: Histogram of observed and simulated Variant state bouts.

Figure S2: Histogram of observed and simulated Variant state bouts.

Variant State Summary

Table S6: Summary of Variant state bout duration in dive cycles and hours, for both observed data and simulations based on the fitted HHMM (in which no MFAS exposure occurs after initiation of Variant state).

Type	Metric	median	IQR	mean	sd	min	max
Observed	Dive Cycles	2.0	3.0	3.8	5.4	1.0	37.0
Observed	Duration (h)	9.0	9.2	10.9	11.5	1.0	72.4
Simulated	Dive Cycles	3.0	4.0	3.6	3.3	1.0	29.0
Simulated	Duration (h)	7.5	10.7	10.7	10.5	0.3	109.6

Time-series plots for each tag deployment

Dive Profile Plots

Below are dive trace time-series plots for all whales with RLs and coarse-scale state indicated.

In these plots:

• Grey shading indicates a dive cycle that was classed as Variant state
• Received levels are shown in lower plots. The lines indicate cumulative SEL (cumulative by dive cycle; for the 5-minute scale, SEL is cumulative across a single dive cycle up to the end of the current 5-minute interval). Dots indicate RMS RL.
• Depths shown are the medians in 5-minute intervals (so may not reach the surface, etc.)
• Colors indicate the fine-scale (5-minute) states
• In interactive plots (in html output file format),
  • You can zoom!
  • Mouse over the RL dot to get the exact RL value

Figure S3: Dive depth profile for tag Zica-20191012-144029, with HHMM state and sound exposure information. Open circles indicate times echosounders were detected on the tag record.

Figure S4: Dive depth profile for tag Zica-20191012-145101, with HHMM state and sound exposure information. Symbols indicate times various sounds were detected on the tag record: open circles for echosounders and Xs for impulsive sounds.

Figure S5: Dive depth profile for tag Zica-20191111-94810, with HHMM state and sound exposure information. Symbols indicate times various sounds were detected on the tag record: open circles for echosounders and Xs for impulsive sounds.

Figure S6: Dive depth profile for tag Zica-20191117-195993, with HHMM state and sound exposure information. Open circles indicate times echosounders were detected on the tag record.

Figure S7: Dive depth profile for tag Zica-20211112-94819, with HHMM state and sound exposure information.

Figure S8: Dive depth profile for tag Zica-20211113-195993, with HHMM state and sound exposure information.

Figure S9: Dive depth profile for tag Zica-20220112-195994, with HHMM state and sound exposure information. Open triangles indicate times orca sounds were detected on the tag record.

Figure S10: Dive depth profile for tag Zica-20230518-233391, with HHMM state and sound exposure information. Xs indicate times impulsive sounds were detected on the tag record.

Figure S11: Dive depth profile for tag Zica-20230519-232950, with HHMM state and sound exposure information. Symbols indicate times various sounds were detected on the tag record: open circles for echosounders and Xs for impulsive sounds.

Figure S12: Dive depth profile for tag Zica-20230723-233394, with HHMM state and sound exposure information. Xs indicate times impulsive sounds were detected on the tag record.

Figure S13: Dive depth profile for tag Zica-20230723-233395, with HHMM state and sound exposure information. Symbols indicate times various sounds were detected on the tag record: open circles for echosounders and Xs for impulsive sounds.

Figure S14: Dive depth profile for tag Zica-20240227-233396, with HHMM state and sound exposure information. Symbols indicate times various sounds were detected on the tag record: open circles for echosounders and Xs for impulsive sounds.

Figure S15: Dive depth profile for tag Zica-20240227-240128, with HHMM state and sound exposure information.

Figure S16: Zoomed-in view of data from tag Zica-20191012-144029, from 10/13/2019 05:58 until 10/14/2019 13:14 UTC.

Figure S17: Zoomed-in view of data from tag Zica-20191012-145101, from 10/13/2019 05:58 until 10/14/2019 13:14 UTC.

Dive Cycle Plots

Below are time-series plots for each whale, showing dive-cycle-scale observations (with “dive cycle number” on x axis). MFAS levels and coarse-scale state (decoded using the fitted HHMM and the Viterbi algorithm) are also indicated.

Figure S18: HHMM input data streams for tag Zica-20191012-144029 at the dive-cycle timescale, with decoded states and MFAS exposure levels.

Figure S19: HHMM input data streams for tag Zica-20191012-145101 at the dive-cycle timescale, with decoded states and MFAS exposure levels.

Figure S20: HHMM input data streams for tag Zica-20191111-94810 at the dive-cycle timescale, with decoded states and MFAS exposure levels.

Figure S21: HHMM input data streams for tag Zica-20191117-195993 at the dive-cycle timescale, with decoded states and MFAS exposure levels.

Figure S22: HHMM input data streams for tag Zica-20211112-94819 at the dive-cycle timescale, with decoded states and MFAS exposure levels.

Figure S23: HHMM input data streams for tag Zica-20211113-195993 at the dive-cycle timescale, with decoded states and MFAS exposure levels.

Figure S24: HHMM input data streams for tag Zica-20220112-195994 at the dive-cycle timescale, with decoded states and MFAS exposure levels.

Figure S25: HHMM input data streams for tag Zica-20230518-233391 at the dive-cycle timescale, with decoded states and MFAS exposure levels.

Figure S26: HHMM input data streams for tag Zica-20230519-232950 at the dive-cycle timescale, with decoded states and MFAS exposure levels.

Figure S27: HHMM input data streams for tag Zica-20230723-233394 at the dive-cycle timescale, with decoded states and MFAS exposure levels.

Figure S28: HHMM input data streams for tag Zica-20230723-233395 at the dive-cycle timescale, with decoded states and MFAS exposure levels.

Figure S29: HHMM input data streams for tag Zica-20240227-233396 at the dive-cycle timescale, with decoded states and MFAS exposure levels.

Figure S30: HHMM input data streams for tag Zica-20240227-240128 at the dive-cycle timescale, with decoded states and MFAS exposure levels.

Variant Timecourse

We can also consider dive-cycle characteristics of variant dive cycles as a function of dive-cycle number within the sequence of several variant dive cycles. This could help investigate the question of whether there might be differences between “initial” and “later” variant behavior.

Figure S31: Dive-cycle characteristics of variant dive cycles as a function of dive-cycle number, within the sequence of several variant dive cycles.

Depth Distribution of 5-minute States

Figure S32: Depth distribution of 5-minute intervals, by dive-cycle and 5-minute state. Color indicates MFAS cSEL.

Figure S33: Depth as a function of MFAS cSEL for 5-minute intervals, by dive-cycle and 5-minute state.

HHMM Model Validation & Interpretation

Stationary Distributions

Based on the transition probability matrices, we can compute stationary distributions based on the model, which present the proportion of “time” whales would be expected to spend in each state in the long run. (“Time” because it’s the proportion of time-steps, which for the coarse dive-cycle states is not exactly the same as the duration of dive cycles varies.)

Figure S34: Stationary state distribution at the dive-cycle scale. The values show the expected proportion of dive cycles spent in each state if the MFAS exposure level was perpetually at a certain value.

Figure S35: Stationary state distribution at the dive-cycle scale. The values show the expected proportion of dive cycles spent in each state if the MFAS exposure level was perpetually at a certain value.

Lag plots

These plots may sometimes help verify the number of states in the data, as discussed in Lawler et al. 2019 and Sidrow et al. 2022

Figure S36: Lag plot for 90th percentile of MSA.

Figure S37: Lag plot for fluke stroke rate.

Figure S38: Lag plot for circular standard deviation of heading.

Model Pseudoresiduals

Computing pseudo-residuals... 

Figure S39: HHMM pseudo-residuals.

Likelihood Weighting Simulation Results

Case 1: True Model Includes MFAS Effect

AIC and likelihood results

Figure S40: By what margin would model selection using AIC select the true model (with MFAS effect), with and without duration-weighting applied to the likelihood?

Table S7: Proportion of simulations where the difference in AIC (model with MFAS minus model without) exceeded 6, when the true model was one with MFAS effect.

Weighting?	Proportion dAIC > 6
No	0.81
Yes	1.00

Confidence Interval Coverage

Table S8: Confidence interval coverage in simulations, for simulations in which the true model included an effect of MFAS on the transition rates. “T->V” is the probability of transition from Typical to Variant state, and “V->T” is Variant to Typical.

Model Name	N Simulations	CI Coverage (%; P(T->V))	CI Coverage (%; P(V->T))	Mean Absolute Error (%; P(T->V))	Mean Absolute Error (%; P(V->T))
rl_coarse	101	96.0	43.10	30.6	290
rl_coarse_wt	101	26.7	8.54	32.1	421

Figure S41: Parameter estimates and 95% confidence intervals for the parameter measuring the effect of MFAS on transition from Typical to Variant state. Dotted horizontal line shown the true value of the parameter.

Figure S42: Parameter estimates and 95% confidence intervals for the parameter measuring the effect of MFAS on transition from Variant to Typical state (note, this one is not estimated well because of the small size of the dataset). Dotted horizontal line shown the true value of the parameter.

Power

Based on CIs, how often would we conclude there IS an MFAS effect (when there really is)?

Table S9: Power to detect MFAS effect when it is really present.

Model Name	Power (%, P(T->V))	Power (%, P(V->T))
rl_coarse	75.2	32.3
rl_coarse_wt	99.0	100.0

Case 2: True Model Excludes MFAS Effect

AIC and likelihood results

Figure S43: By what margin would model selection using AIC select the true model (without MFAS effect – so a small AIC difference would be hoped for), with and without duration-weighting applied to the likelihood?

Table S10: Proportion of simulations where the difference in AIC (model with MFAS minus model without) exceeded 6, when the true model was one without MFAS effect.

Weighting?	Proportion dAIC > 6
No	0.008849558
Yes	0.882882883

Confidence Interval Coverage

Table S11: Confidence interval coverage in simulations, for simulations in which the true model did not include an effect of MFAS on the transition rates. “T->V” is the probability of transition from Typical to Variant state, and “V->T” is Variant to Typical.

Model Name	N Simulations	CI Coverage (%; P(T->V))	CI Coverage (%; P(V->T))
rl_coarse	113	97.3	96.4
rl_coarse_wt	112	25.9	19.6